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    (ω′, [ω], Ĉ′) for (a) ERBE/ERA-40 data and (c) ERBE/NCEP2 data. The shaded bins represent significant differences to the ERBE/ERA-40 data results on the 95% level. (b) The standard deviation about the mean ERBE/ERA-40 values. Units are Pa s−1 × 100 and W m−2, respectively.

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    Same as in Fig. 1, but for ([h], h′, Ĉ′) distributions. Units are % and W m−2, respectively.

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    ([ω], ω′, Ĉ′) for the IPCC models. Units are Pa s−1 × 100 and W m−2, respectively. The shaded bins represent significant differences to the ERBE/ERA-40 data results on the 95% level.

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    Dependence of total SWCRF Ĉ on total ω, under three different regimes of [ω] for the ERA-40/ERBE dataset.

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    Correlation r between the IPCC model results and the ERBE/ERA-40 observational data for the [ω] regimes. The correlation between ERBE/NCEP2 and ERBE/ERA-40 data is also plotted.

  • View in gallery

    (a) MSDs between the IPCC model results and the ERBE/ERA-40 observational data for the [ω] regimes. The MSD between ERBE/NCEP2 and ERBE/ERA-40 data is also plotted. (b) Same as in (a), but the MSD is weighted by the pdf of [ω].

  • View in gallery

    PDF of (a) ω′ and (b) the mean climatological vertical velocity [ω] for IPCC models (lines with symbols) and ERA-40 data (black line). (c) The pdf × 100 of the ([ω], ω′) bins are plotted for the ERA-40 data.

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    ([h], h′, Ĉ′) for the IPCC models. Units are % and W m−2, respectively. The shaded bins represent significant differences to the ERBE/ERA-40 data results on the 95% level.

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    Correlation r between the IPCC model results and the ERBE/ERA-40 observational data for the [h] regimes. The correlation between ERBE/NCEP2 and ERBE/ERA-40 data is also plotted.

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Relationship between Shortwave Cloud Radiative Forcing and Local Meteorological Variables Compared in Observations and Several Global Climate Models

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  • 1 International Pacific Research Center, University of Hawaii at Manoa, Honolulu, Hawaii
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Abstract

The relations between local monthly mean shortwave cloud radiative forcing and aspects of the resolved-scale meteorological fields are investigated in hindcast simulations performed with 12 of the global coupled models included in the model intercomparison conducted as part of the preparation for Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4). In particular, the connection of the cloud forcing over tropical and subtropical ocean areas with resolved midtropospheric vertical velocity and with lower-level relative humidity are investigated and compared among the models. The model results are also compared with observational determinations of the same relationships using satellite data for the cloud forcing and global reanalysis products for the vertical velocity and humidity fields. In the analysis the geographical variability in the long-term mean among all grid points and the interannual variability of the monthly mean at each grid point are considered separately. The shortwave cloud radiative feedback (SWCRF) plays a crucial role in determining the predicted response to large-scale climate forcing (such as from increased greenhouse gas concentrations), and it is thus important to test how the cloud representations in current climate models respond to unforced variability.

Overall there is considerable variation among the results for the various models, and all models show some substantial differences from the comparable observed results. The most notable deficiency is a weak representation of the cloud radiative response to variations in vertical velocity in cases of strong ascending or strong descending motions. While the models generally perform better in regimes with only modest upward or downward motions, even in these regimes there is considerable variation among the models in the dependence of SWCRF on vertical velocity. The largest differences between models and observations when SWCRF values are stratified by relative humidity are found in either very moist or very dry regimes. Thus, the largest errors in the model simulations of cloud forcing are prone to be in the western Pacific warm pool area, which is characterized by very moist strong upward currents, and in the rather dry regions where the flow is dominated by descending mean motions.

Corresponding author address: M. Stowasser, IPRC/SOEST, University of Hawaii at Manoa, 1680 East–West Rd., Post Bldg. 401, Honolulu, HI 96822. Email: stowasse@hawaii.edu

Abstract

The relations between local monthly mean shortwave cloud radiative forcing and aspects of the resolved-scale meteorological fields are investigated in hindcast simulations performed with 12 of the global coupled models included in the model intercomparison conducted as part of the preparation for Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4). In particular, the connection of the cloud forcing over tropical and subtropical ocean areas with resolved midtropospheric vertical velocity and with lower-level relative humidity are investigated and compared among the models. The model results are also compared with observational determinations of the same relationships using satellite data for the cloud forcing and global reanalysis products for the vertical velocity and humidity fields. In the analysis the geographical variability in the long-term mean among all grid points and the interannual variability of the monthly mean at each grid point are considered separately. The shortwave cloud radiative feedback (SWCRF) plays a crucial role in determining the predicted response to large-scale climate forcing (such as from increased greenhouse gas concentrations), and it is thus important to test how the cloud representations in current climate models respond to unforced variability.

Overall there is considerable variation among the results for the various models, and all models show some substantial differences from the comparable observed results. The most notable deficiency is a weak representation of the cloud radiative response to variations in vertical velocity in cases of strong ascending or strong descending motions. While the models generally perform better in regimes with only modest upward or downward motions, even in these regimes there is considerable variation among the models in the dependence of SWCRF on vertical velocity. The largest differences between models and observations when SWCRF values are stratified by relative humidity are found in either very moist or very dry regimes. Thus, the largest errors in the model simulations of cloud forcing are prone to be in the western Pacific warm pool area, which is characterized by very moist strong upward currents, and in the rather dry regions where the flow is dominated by descending mean motions.

Corresponding author address: M. Stowasser, IPRC/SOEST, University of Hawaii at Manoa, 1680 East–West Rd., Post Bldg. 401, Honolulu, HI 96822. Email: stowasse@hawaii.edu

1. Introduction

Predictions of climate change due to increasing greenhouse gases under a particular forcing scenario vary considerably among current climate models. For example, the Intergovernmental Panel on Climate Change (IPCC) Third Assessment Report (TAR; Houghton et al. 2001) featured results of global warming simulations from 19 different global coupled atmosphere–ocean models. The equilibrium climate sensitivity to a doubling of atmospheric CO2 diagnosed from global warming integrations varied by a factor of as much as 3 among the models. Much of the variation in the climate sensitivity of the global-mean surface temperature is attributable to differences in how the clouds respond to climate forcing (e.g., Senior 1999; Yao and Del Genio 1999). Cess et al. (1996) showed that there was considerable variability in both the shortwave and longwave cloud feedbacks in global warming simulations performed with a large number of different global models. In a recent study Stowasser et al. (2006) performed a detailed diagnosis of the global and local feedbacks apparent in global warming simulations with versions of the National Center for Atmospheric Research (NCAR) Climate System Model and the Canadian Centre for Climate Modelling and Analysis (CCCma) model. The clear-sky feedbacks were similar among the models considered, but the cloud feedbacks varied considerably in both geographical pattern and global-mean value. In terms of the sensitivity of the global-mean surface temperature, almost all the differences among the models could be attributed to differences in the shortwave cloud feedbacks in the tropical and subtropical regions: the NCAR models have a net negative shortwave cloud feedback while the CCCma model examined has a positive shortwave cloud feedback. The result is a sensitivity of global-mean surface temperature in the CCCma model that is almost twice that in the NCAR models.

Given the importance of the cloud feedbacks for the sensitivity of local and global-mean climate, it would be useful to understand why individual models differ in the regard and also to have some test of how realistic are the cloud feedbacks simulated in a particular model. Conceptually it would be useful if the differences in the cloud feedbacks seen in warming simulations with two different models could be separated into (i) a component due to differences in how the model circulation fields change, and (ii) a component attributable to the different response of the cloud parameterizations to a given circulation change. In practice, this kind of separation cannot be done cleanly since the way the cloud parameterization responds to changes in the resolved meteorological fields affects the way the circulation itself changes in response to the imposed climate forcing. Despite this, however, there have been some recent papers (e.g., Bony et al. 1997, 2004; Norris and Weaver 2001; Williams et al. 2003) that have presented techniques to assess cloud behavior in particular dynamical regimes in order to separate the effects of parameterized cloud physical processes and changes in the large-scale dynamical circulation.

Here we will attempt to use a somewhat similar approach to assess in a simple manner the response of the cloud radiative forcing (CRF) in a number of coupled global climate model simulations meant to be representative of the late twentieth century. The record of the actual trends in climate and cloud fields over recent decades is of rather limited value as a test of cloud effects in climate models, since the trends have been fairly modest and the satellite record of detailed cloud radiative effects is less than three decades in length. We will consider simulations and observations over just a 5-yr period (1985–89) and so will investigate cloud behavior in relation mainly to natural variability of the large-scale circulation. We will consider here just the behavior of the clouds over tropical and subtropical ocean areas, but within this area we consider how cloud feedbacks vary geographically, as a function of long-term mean circulation, and temporally, as a function of the interannual circulation fluctuations. In particular, the dependence of shortwave cloud radiative forcing (SWCRF) on midtropospheric vertical velocity and lower-tropospheric relative humidity are examined in a large subset of the models participating in the intercomparison being conducted as part of the preparation of the IPCC Fourth Assessment Report (AR4). The performance of the models is compared with observations of the SWCRF from satellites and values of the meteorological fields from global reanalyses.

A brief description of the models and the observational datasets used is given in section 2. Section 3 describes the formalism employed to characterize the relationships between the SWCRF and the meteorological variables and shows some results for the observational datasets. The results for the various models are presented and compared in section 4. A discussion and the conclusions are given in section 5.

2. Models and observational data

Twelve models participating in the IPCC AR4 were used for this study (see Table 1).

Segments of the so-called “twentieth century” runs (20c3m scenario) were analyzed. These runs began from spunup preindustrial initial conditions appropriate for some time in the late nineteenth century and then were integrated forward through 1999, with the concentration of long-lived greenhouse gases and atmospheric aerosols being specified with realistic time series. The details of the climate forcing imposed were left to the individual modeling groups. So, for example, only some of the model 20c3m simulations included volcanic stratospheric aerosol.

The atmospheric components of six of the coupled models employ spectral numerics in the horizontal and for these models the resolution ranges from R15 to T106 (see Table 1). The other six models have some kind of gridpoint representation of the atmospheric dynamics and employ resolutions ranging from 2.5° × 2.0° to 4° × 5°. The various models use between 9 and 56 vertical levels. The cloud fraction schemes employed by the various models can be categorized broadly into three groups: relative humidity–based schemes, statistical total water schemes, and prognostic cloud fraction schemes. Five models use a prognostic scheme [the Geophysical Fluid Dynamics Laboratory Coupled Model Versions 2.0/2.1 (GFDL-CM2.0/2.1), the Model for Interdisciplinary Research on Climate Version 3.2 (MIROC3.2hires/medres), and the NCAR Community Climate System Model Version 3 (CCSM3)]; five use relative humidity–based schemes [the CCCma Third Generation Coupled Global Climate Model (CGCM3.1), the Goddard Institute for Space Studies (GISS) models GISS-EH/ER, the Flexible Global Ocean–Atmosphere– Land System (FGOALS-g1.0), and the Instituto Nacional de Meteorología Coupled Model Version 3.0 (INM-CM3.0)]; and only two use a statistical scheme [the Centre National de Recherches Meteorologiques Coupled Model Version 3 (CNRM-CM3) and L’Institut Pierre-Simon Laplace Coupled Model Version 4 (IPSL-CM4)]. For detailed descriptions of the models and their physical parameterizations we refer to the references given in Table 1.

The IPCC models are evaluated through comparisons with a combination of satellite and reanalysis sets. The satellite observations are taken from the Earth Radiation Budget Experiment (ERBE) dataset (Barkstrom 1984), and our principal source of the corresponding meteorological fields is the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) dataset (Simmons and Gibson 2000). We also compare results obtained with the ERA-40 data with those from the National Centers for Environmental Prediction (NCEP) reanalysis-2 data, which is based on the widely used NCEP–NCAR reanalysis (Kalnay et al. 1996). These data sources provide values on 2.5° × 2.5° latitude–longitude grids, but the grids are offset. To simplify the analysis all data are interpolated to the grid of the ERBE data. All analysis of observational and model data is based on monthly mean values interpolated to this 2.5° × 2.5° grid. We analyze data at all grid points over the ocean and in the 30°S–30°N latitude band for the 5-yr period from January 1985 to December 1989. This period starts over two years after the 1982 El Chichón volcanic eruption and ends before the 1991 eruption of Mt. Pinatubo, and was selected to minimize any complications from effects of stratospheric aerosols.

Barkstrom et al. (1989) and Harrison et al. (1990) have attempted to quantify the error in the ERBE top-of-the-atmosphere (TOA) fluxes. For the shortwave fluxes Barkstrom et al. (1989) estimated accuracy for the monthly mean values of shortwave flux of ±5 W m−2 while Harrison et al. (1990) suggest errors slightly larger than this. Comparisons of fluxes using the ERBE and newer single scanner footprint algorithms with empirical angular distribution models (ADMs) found larger errors in the ERBE data. In a study by Loeb et al. (2003) the SW cloud radiative forcing differences estimated from instantaneous ERBE-like and SSF TOA fluxes depend on the optical thickness of the cloud, and range from +10 to −15 W m−2. The root-mean-square error differences in CRF between the ERBE-like and SSF TOA fluxes are typically 7–8 W m−2 in the SW.

We will employ relative humidity and vertical velocity fields from the ERA-40 and NCEP2 reanalyses. The use of gridded meterological reanalyses to provide the vertical velocity and humidity fields for our analysis introduces some limitations. Over the ocean areas where our analysis will be applied, there are very few in situ observations of upper air available, and the fields in the reanalyses are an indirect diagnostic produced using an assimilation scheme in a particular numerical model. This is particularly the case for the vertical velocity, which is nowhere directly observed. The uncertainty in the reanalyses products is one motivation for comparing the analysis for two different sets of reanalyses data. The differences between the ERA-40 and NCEP2 reanalysis fields provide at least a lower bound on the uncertainty.

Trenberth and Guillemot (1995, 1998) compared the precipitable water over tropical and subtropical ocean areas measured by SSM/I satellite microwave observations with ECMWF and NCEP analyses, and the NCEP–NCAR reanalyses. These datasets are predecessors of the reanalyses used in our present study. This comparison provides a reasonably direct check on the uncertainty in the lower-tropospheric humidity, as this generally dominates the total precipitable water column. Correlations of the time series of monthly mean water column at individual grid points between the analyses and the satellite observations are generally high (more than 0.9 over much of the tropical and subtropical ocean areas). However, it should be noted that these correlations include the annual cycle as well as the interannual fluctuations, which are the focus of the present analysis. Both the ECMWF and NCEP analyses do have some consistent, if modest, biases relative to the satellite data, showing ∼10% lower columns than the satellites near the equator and about ∼10% larger columns in the subtropics.

We have no comparable observational dataset for 500-hPa vertical velocity ω. One possibly useful point to make, however, is that the overall distribution of both the climatological mean and the interannual variations of ω is reasonably similar in the reanalyses and in the GCMs considered here. In fact we will demonstrate this later in the present paper (see Fig. 7). So at least there is no evidence for a significant systematic suppression or enhancement of the actual vertical velocity in the reanalyses.

3. Analysis method

The basic idea is to stratify cloud data according to physically based regime indicators X, such as the isobaric coordinate vertical velocity ω, and the relative humidity h.

We define the SW component of the CRF as the difference between the solar radiation absorbed in the atmospheric/surface column in actual and clear-sky conditions; this can be determined from TOA observations (e.g., Coakley and Baldwin 1984). Let C be the SW component of the CRF. Following Bony et al. (2004) the regime indicators are binned into a series of regimes corresponding to different values of X:
i1520-0442-19-17-4344-e1
Considering mean values Ĉj in the defined regime intervals (1) can be rewritten as
i1520-0442-19-17-4344-e2
to give the area-averaged value C and the probability distribution function (PDF) pj, which holds Σjpj = 1. This decomposition can be done for all different kinds of representation of the climate (e.g., using a long-term average, monthly mean values, or interannual variations).

We are interested in the relationship between the time-mean value of X and C as well as the response of C to deviations, X′, from this mean.

We want to consider only the interannual fluctuations, so the X′ and C′ values have been deseasonalized. We define mean values of C and X for every grid point and calendar month, [Xki] and SWCRF [Cki], where i = 1, . . . , N, k = 1, . . . , 12, and N is the number of grid points. The variations from the mean are constructed by subtracting the monthly climatology from each month of the data Xi = Xki − [Xki]. The corresponding deviations Ci are constructed in a analogous way. Both variables [Xki] and Xi are binned into intervals so that
i1520-0442-19-17-4344-eq1

The Ci values are averaged for all 30°S–30°N ocean points falling within each ([Xl], Xm) category and for each month in the 5-yr analysis period. The resulting average values of SWCRF, Ĉ′, can then be displayed in a contour plot as a function of the variations X′ and mean [X]. Figure 1a illustrates the approach, using monthly mean values of 500-hPa large-scale vertical velocities from ERA-40 and the SWCRF determinations from the ERBE data.

The contours are plotted for each part of [ω] and ω′ space that is occupied by at least a single grid point of data for at least one month in the full 5-yr period. The contours in Fig. 1b give the standard deviation σ about the mean values. Larger variations are generally found for large upward motion anomalies in regimes with modest negative values of [ω]. The smallest values of σ are found in regions with strong downward mean motions.

The ascending branches of the Hadley–Walker circulation, that occur mostly over the warmest portions of the Tropics, correspond to negative values of [ω], while regions of large-scale subsidence correspond to positive values of [ω]. The bin interval used for both [ω] and ω′ is 0.02 Pa s−1. For locations where there is a weak mean [ω], the observations in Fig. 1 reveal a linear relationship between Ĉ′ and ω′. For either stronger mean ascending or stronger mean descending velocities, the relationship between ω′ and Ĉ′ gets weaker. In locations with strong upward mean motions, convection may lead to extensive cloud cover and the interannual fluctuations in ω may not be able to affect this much. Similarly regions of strong descending mean motion may be dry and relatively cloud free even in the presence of significant interannual fluctuations in ω′. The dominance of mean descending motion over ω′ effects is evident in Fig. 1 where Ĉ′ values are less than 5 W m−2 even for large ω′ when [ω] is greater than about 0.04 Pa s−1.

The strongest dependence of Ĉ′ on ω′ occurs for fairly weak negative [ω], although there is considerable asymmetry between the positive and negative ω′ behavior. Notably the most negative values of Ĉ′ are about −40 W m−2 and found for strong upward motion anomalies in locations where [ω] is small. The largest positive values of Ĉ′ occur for strong downward anomalies in regions of moderate mean rising motion ([ω] ∼0.04 Pa s−1).

To test the robustness of the described behavior of Ĉ′ in the ERA-40/ERBE dataset the analysis was repeated with the ω field taken from the NCEP2 reanalysis data. The results are given in Fig. 1c. Overall the results look very similar reproducing the two “semicircles” in Fig. 1a. However, using the ERA-40 data reveals a stronger dependence of the Ĉ′ on |ω′| especially for modest [ω] values. To test if the differences between the two datasets are statistical significant an unequal variance two-sample t test (e.g., Wilks 1995)
i1520-0442-19-17-4344-e3
was performed for each bin. The shading represents bins with a 95% significant level. In most of the domain the differences are not significant. However, due to the large number of data points in some modest ([ω], ω′) bins statistical significant differences are found although ĈERAĈNCEP is small. Conversely, the moderately large differences in the more extreme regimes are not significant, because the data are sparse. Bins with less than five data points have been marked as not significant to account for the noise in these bins.

The analysis of ERBE and ERA data just described was repeated in order to examine the behavior of Ĉ′ as a function of long-term mean and variations in relative humidity. The SWCRF is mostly dominated by low and middle clouds except in regions of deep convection, where very bright stratiform anvils may contribute significantly to the SWCRF. Therefore, we use the mean relative humidity h in a layer between the surface and 700 hPa as the regime indicator in this case. In Fig. 2a the relationships between [h]-h′ and Ĉ′ are shown for the ERBE/ERA-40 data. The strongest dependence of Ĉ′ on h′ is found for [h] ≈ 70%.

The response is slightly asymmetric with largest negative values of Ĉ′ of around −40 W m−2 for large positive h′, but maximum positive values of only 20 W m−2 for large negative h′. With decreasing mean humidity [h] the SWCRF changes with h′ are very modest. For [h] < 50% |Ĉ′| is always smaller than 10 W m−2.

Again, the contours in Fig. 2b give the the standard deviation about the mean values. The variations are quite similar in the whole ([h], h′) domain. Figure 2c shows the analysis repeated using the NCEP2 relative humidity fields. In most of the domain the differences to the results obtained with the ERA-40 data are small. However, for moist mean regimes ([h] > 60%) and positive h′, using the ERBE/ERA-40 dataset results in a stronger dependence of Ĉ′ on h′. The t test shows that these differences are indeed statistical significant on a 95% level represented by the shading of bins. Nevertheless, the overall structure shows a very close resemblance.

4. Results for the IPCC models

The identical analysis was applied to the monthly mean data from the 1985–89 segments of the 20c3m IPCC runs as retrieved from the IPCC public archive.

a. Relationships with ω

In Fig. 3 the results for dependence of SWCRF on ω are depicted in the same format as in Fig. 1.

Immediately apparent is a wide range of behavior among the 12 models considered. None of the models is able to reproduce well the full observed picture in Fig. 1. The model Ĉ′ is generally a strong function of only ω′, and the complicated dependence of Ĉ′ on [ω] seen in the observations is much less apparent. Notably, the two semicircles apparent in the contours in Fig. 1 are mainly absent in the model results, or are apparent only for larger values in the magnitude of the [ω] and ω′ fields. The GCM that comes closest to reproducing the overall pattern in Fig. 1 appears to be the IPSL-CM4 model.

It is interesting that the SWCRF seems to depend in a complex way with both [ω] and ω′, and not just on the total vertical velocity for each month [ω] + ω′. In Fig. 4 Ĉ = [Ĉ] + Ĉ′ is plotted over the total vertical velocity. To illustrate the dependence on [ω] the relationship of Ĉ with ω is shown for three different regimes: rising motions with [ω] < 0.04 Pa s−1, neutral (−0.04 < [ω] < 0.04 Pa s−1), and downward motions with [ω] > 0.04 Pa s−1. In all three regimes different relationships between Ĉ and ω are found. For mean subsidence regimes the dependence of Ĉ on ω is very weak; however, for mean upward rising motion regimes Ĉ holds a linear relationship with ω.

Most of the models show qualitatively the same behavior as the observations in the regime of small values of the magnitude of ω′ but even here there is quite a range in the strength of dependence of the SWCRF on ω′.

A regression model Ĉ′ = f (ω′, [ω])+ϵ was fitted to the observed and modeled ([ω], ω′, Ĉ′) distributions by a least squares method. The fitted model has the form f (ω′, [ω]) = m1 + m2ω′ + m3[ω] + m4ω′[ω] + m5ωω′ + m6[ω][ω]. The fit was restricted to the region for which ω′ and [ω] are between −0.06 and +0.06 Pa s−1 and each ω′-[ω] was weighted equally. The resulting coefficients mi for all the models and the observations are given in Table 2. The coefficients m5 and m6 are generally very small and therefore not listed.

The strength of the dependence of Ĉ′ on ω′ is reflected by m2. The two observational datasets are in good agreement, although the use of the NCEP2 data shows a slightly weaker Ĉ′-ω′ dependence. The model results range from a strong underestimation (FGOALS-g1.0) to a strong overestimation of m2 (INM-CM3.0). The two GISS models and the IPSL-CM4 are closest to the observational values of m2. A good agreement between the NCEP and ERA-40 data is also seen for the coefficient m4, which represents the nonlinear structure of the Ĉ′ response. The m4 term is underestimated by almost all the models.

Table 2 shows there is a very considerable range of the SWCRF dependence on vertical velocity in the various models, with m2 varying by a factor of more than 4 or by more than 300 W m−2 Pa−1s. How serious are the implications of this for our confidence in model forecasts of climate change? Some perspective on this issue may be obtained by analysis of the global warming experiments described in Stowasser et al. (2006). In particular, consider the experiment reported there in which the solar constant was increased by 5% (resulting in a global-mean climate forcing of about 12 W m−2) in version 2.0.1 of the NCAR Community Climate System Model. The long-term mean response includes an El Niño–like warming structure in the tropical Pacific, which involves significant geographical variations in the radiative and dynamical response. The change in 500-hPa vertical velocity along the equator has contrasts as large as 0.04 Pa s−1 while the TOA radiative response has variations of the order of 20 W m−2. The ratio of these two scales is of the order of 500 W m−2 Pa s −1. This is similar to the uncertainty in m2 among the models considered here. This suggests that the degree of uncertainty in the SWCRF documented here is quite significant.

Some further simple measures of the congruence of the model results in Fig. 3 and observations in Fig. 1 have been computed. Table 3 shows correlation coefficients of the Ĉ′ values calculated between observations and each model, weighting each occupied [ω]′ bin equally.

Also computed is a mean-square-difference (MSD) in Ĉ′ between model and observational results, again weighting each [ω]′ bin equally. The correlations are reasonably large for most of the models, reflecting the good agreement in the functional dependence for the neutral and modest rising/downward motion regimes seen in Fig. 3. As a point of reference the correlation and MSDs between the ERBE/ERA-40 and ERBE/NCEP2 results are given in Table 3 too.

From this analysis none of the three cloud-scheme classes stands out in its ability to simulate the features of the observations. For example among the models using a cloud scheme based on relative humidity, are the ones that show both the strongest and weakest dependence of Ĉ′ on ω′ for modest [ω].

The results for the IPSL-CM4 model show both the highest correlation and lowest MSD with observations. The cloud cover and in-cloud water of this model are deduced from the large-scale total water and moisture at saturation using a PDF for the subgrid-scale total water. This PDF is described through a generalized lognormal function bounded to 0, following Bony and Emanuel (2001). The PDF moments are diagnosed interactively from the condensed water predicted by the convection scheme at the subgrid scale and from the large-scale degree of saturation of the atmosphere.

Similar correlations and MSD values have been computed as functions of [ω], weighting each occupied ω′ bin equally. The results for the correlation coefficients for all the models are shown in Fig. 5 and for the MSD values in Fig. 6. The correlation and MSD values between the two reanalysis are also plotted in these figures revealing a reasonable good agreement.

Figure 5 shows that all the models fail rather severely in the regime where mean subsidence exceeds 0.04 Pa s−1. There is also disagreement among all models and observations for regions with strong mean ascent, although the disagreement is less severe than for the regions of strong mean descent. Differences in the performance of the various models are apparent once again from examination of the MSD values (see Fig. 6). Most of models show an increase in the MSD for [ω] smaller than −0.06 Pa s−1. No model stands out in its ability to reproduce the observed structure over the whole range of [ω]. For example, the GFDL-CM2.0 model exhibits very small MSD for modest rising motion conditions. However, for stronger rising motion situation the MSD rapidly increases. On the other hand, the MIROC3.2(hires) exhibits very low MSD also for [ω] < −0.06 Pa s−1 but the performance in the modest [ω] regimes is much poorer. In Fig. 6b the MSD are weighted by the pdf of [ω] for each individual model and the ERBE/ERA-40 data reflecting more the errors of area-weighted averages. In this case the largest differences are found for regions with modest subsidence.

The suite of models considered here includes two versions of the MIROC3.2 model that differ just by their horizontal and vertical resolution (T106L56 versus T42L20). When the SWCRF data from these two models are stratified by [ω] and ω′ as we have done, there is almost no difference in the results. In addition, we can see no clear connection between how well the other models considered have performed in representing SWCRF and the spatial resolution employed. Without carrying out controlled experiments by isolating individual physical parameterization components, it is difficult to pinpoint the source of the model differences.

The biggest discrepancies in the model SWCRF dependence on [ω] and ω′ occur for large absolute values of either (or both) [ω] and ω′. The more extreme regimes of [ω] correspond to regions of either intense convective activity or of very strong static stability and subsidence. To see how well the models simulate the range of variation of [ω] and ω′, Fig. 7a shows the number of monthly gridpoint values that fell within the various ω′ bins over the full 5-yr period, and Fig. 7b shows the distribution of the number of grid points as a function of the mean climatological vertical velocity, [ω].

Individual model results and the ERA-40 reanalysis values are both plotted. The overall range of variation in both [ω] and ω′ is fairly similar among the models, and the model results generally agree reasonably well with the ERA-40 data. The biggest discrepancy is in the distribution of the time-mean vertical velocity, where the ERA-40 distribution appears shifted slightly to positive [ω] values. Most of the grid points have [ω] between −0.06 and +0.06 Pa s−1, but there are a few percent of grid points with stronger mean rising motion and [ω] < −0.06 Pa s−1 (see Fig. 7c).

b. Relationship with relative humidity

In Fig. 8 the results for the Ĉ′ as a function of mean and variations in relative humidity are shown for 9 of the 12 models considered earlier.

These models were selected simply because there were monthly mean relative humidity values available. In general the models are able to capture the basic structure seen in Fig. 2. However, the maximum of Ĉ′ for large [h] is clearly underestimated by five of the models [FGOALS-g1.0, INM-CM3.0, IPSL-CM4, MIROC3.2(hi/medres)]. Most of these models also underestimate Ĉ′ in the other [h] regimes. The other four models tend to overestimate the response, especially in the dry (small [h]) regimes.

We calculate correlation coefficients and MSD between model results and observations for the data stratified by h, in just the same manner as for the vertical velocity described above. The right columns in Table 3 give the r and MSD values when calculated over all [h] and h′. In this case the two GFDL models, CM2.0 and CM2.1, appear to display the closest fit to the observations in both the correlation and MSD measures. These two models and the CNRM-CM3 reveal similar or even smaller MSDs relative to the ERA-40/ERBE observations than in the ERBE-NCEP2/ERA-40 comparison. It is interesting to note that the IPSL-CM4 with its very good representation of the ([ω], ω′, Ĉ′) distribution shows a much less realistic behavior when the SWCRF values are stratified by low-level humidity.

Figure 9 shows the spatial correlation r for all [h] regimes.

As stated above, a very good representation of the [h]-h′-Ĉ′ relationships is generally found for [h] > 45%, but for dryer mean conditions the correlation drops rapidly. Nevertheless, the corresponding MSD values remain rather small, since in this regime the simulated and observed |Ĉ′| are small (not shown). The correlation between the ERA-40 and NCEP2 results shows high correlation for the whole range of [h] regimes.

5. Conclusions

It seems likely that the biggest uncertainty involved in forecasting climate response to expected anthropogenic forcing lies in the behavior of the cloud feedbacks. Efforts have been made to deduce details of the cloud feedbacks on purely theoretical and empirical bases. For example, Hartmann and Larson (2002) concluded from fundamental considerations of the saturation vapor pressure dependence on temperature and the dependence of emissivity of H2O rotational lines on vapor pressure that the temperature at the detrainment level of tropical anvil clouds and, consequently, the emission temperature will remain constant during climate change. This implies that emission temperatures of tropical anvil clouds and upper-tropospheric water vapor are essentially independent of the surface temperature. The actual sign of anvil cloud feedback has been debated in recent years. Lindzen et al. (2001) propose from analyzing geostationary data over the western tropical Pacific that it is strongly negative, based on inferred decreases in cloud cover with warming coupled with positive net forcing. Lin et al. (2002), on the other hand, using the Tropical Rainfall Measuring Mission (TRMM) satellite measurements over tropical oceans, suggest that a decrease in anvil cloud cover would produce a positive feedback. Del Genio and Kovari (2002) separated the temperature from the vertical velocity dependence in TRMM data and showed that anvil cloud cover actually increases with warming. The feedback depends on the aggregate cloud forcing of optically thick and thin parts of convective systems. So far we have no simple theory that enables us to anticipate how clouds will respond to large-scale climate forcing and have to rely on sophisticated global climate models in which the cloud processes must be parameterized in terms of the resolved meteorological fields. The existing observational record of sustained trends in cloud forcing is of only about a 25-yr duration and thus may be of only limited value in verifying the behavior of the cloud feedbacks as simulated in models.

Here we have tried instead to see how realistically the cloud radiative forcing is simulated in a variety of current models response to aspects of geographical and temporal variability. To limit the scope of the present study we considered only the behavior of the SWCRF over tropical and subtropical ocean areas. We examined this aspect of model performance in the “twentieth century” simulations in the IPCC AR4 model intercomparison. The monthly mean SWCRF values for 2.5° × 2.5° grid squares were first stratified both by the long-term mean midtropospheric vertical velocity at each location and by the interannual anomaly in the vertical velocity for each month. Results were compared with ERBE estimates of the SWCRF and ERA-40 reanalysis values for the vertical velocity.

The range of both the geographical distribution of mean vertical velocity and the space–time variability of the anomalies in the monthly mean is reasonably consistent among the models, and the models agree reasonably well with the ERA-40 data in this regard.

When the SWCRF values are stratified by the mean and anomaly vertical velocity, however, the results vary greatly among the models. The differences among the models are most apparent in the region of extreme rising or sinking motion, but are also substantial even in the range of weak vertical motion. When the SWCRF results are similarly stratified by lower-level relative humidity, there are also substantial differences among the models.

When the model results are compared with the ERBE and ERA-40 data, it was found that there are substantial differences for all models. In terms of vertical velocity, the most notable deficiency is an unrealistically linear dependence of the SWCRF on vertical velocity even in regimes with strong ascending and descending motion. It was also found that for very humid regimes the majority of models tend to underestimate the SWCRF response. At the other extreme, in locations with dry mean conditions, the modeled SWCRF responds too strongly to variations in humidity. Interestingly, the models with the most realistic dependence of SWCRF on vertical velocity are among the less realistic in their simulation of the SWCRF dependence on relative humidity.

The technique presented here is useful for evaluating the cloud radiative feedbacks in sophisticated global climate models. It seems reasonable to expect a model to reproduce well the observed dependence of SWCRF on the meteorological variables discussed here, in order to have much credibility in quantitative forecasting of the cloud responses to expected large-scale climate forcings. The fact that the models in the AR4 intercomparison differ so widely in our measures of SWCRF dependence on meteorological fields is a matter of concern.

Acknowledgments

This research was supported by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) through its sponsorship of the International Pacific Research Center. The authors benefited from a number of illuminating discussions with George Boer. We acknowledge the international modeling groups for providing their data for analysis, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) for collecting and archiving the model data, the JSC/CLIVAR Working Group on Coupled Modelling (WGCM) and their Coupled Model Intercomparison Project (CMIP) and Climate Simulation Panel for organizing the model data analysis activity, and the IPCC WG1 TSU for technical support. The IPCC Data Archive at Lawrence Livermore National Laboratory is supported by the Office of Science, U.S. Department of Energy. The authors thank the editor and anonymous reviewers for a number of valuable comments.

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Fig. 1.
Fig. 1.

(ω′, [ω], Ĉ′) for (a) ERBE/ERA-40 data and (c) ERBE/NCEP2 data. The shaded bins represent significant differences to the ERBE/ERA-40 data results on the 95% level. (b) The standard deviation about the mean ERBE/ERA-40 values. Units are Pa s−1 × 100 and W m−2, respectively.

Citation: Journal of Climate 19, 17; 10.1175/JCLI3875.1

Fig. 2.
Fig. 2.

Same as in Fig. 1, but for ([h], h′, Ĉ′) distributions. Units are % and W m−2, respectively.

Citation: Journal of Climate 19, 17; 10.1175/JCLI3875.1

Fig. 3.
Fig. 3.

([ω], ω′, Ĉ′) for the IPCC models. Units are Pa s−1 × 100 and W m−2, respectively. The shaded bins represent significant differences to the ERBE/ERA-40 data results on the 95% level.

Citation: Journal of Climate 19, 17; 10.1175/JCLI3875.1

Fig. 4.
Fig. 4.

Dependence of total SWCRF Ĉ on total ω, under three different regimes of [ω] for the ERA-40/ERBE dataset.

Citation: Journal of Climate 19, 17; 10.1175/JCLI3875.1

Fig. 5.
Fig. 5.

Correlation r between the IPCC model results and the ERBE/ERA-40 observational data for the [ω] regimes. The correlation between ERBE/NCEP2 and ERBE/ERA-40 data is also plotted.

Citation: Journal of Climate 19, 17; 10.1175/JCLI3875.1

Fig. 6.
Fig. 6.

(a) MSDs between the IPCC model results and the ERBE/ERA-40 observational data for the [ω] regimes. The MSD between ERBE/NCEP2 and ERBE/ERA-40 data is also plotted. (b) Same as in (a), but the MSD is weighted by the pdf of [ω].

Citation: Journal of Climate 19, 17; 10.1175/JCLI3875.1

Fig. 7.
Fig. 7.

PDF of (a) ω′ and (b) the mean climatological vertical velocity [ω] for IPCC models (lines with symbols) and ERA-40 data (black line). (c) The pdf × 100 of the ([ω], ω′) bins are plotted for the ERA-40 data.

Citation: Journal of Climate 19, 17; 10.1175/JCLI3875.1

Fig. 8.
Fig. 8.

([h], h′, Ĉ′) for the IPCC models. Units are % and W m−2, respectively. The shaded bins represent significant differences to the ERBE/ERA-40 data results on the 95% level.

Citation: Journal of Climate 19, 17; 10.1175/JCLI3875.1

Fig. 9.
Fig. 9.

Correlation r between the IPCC model results and the ERBE/ERA-40 observational data for the [h] regimes. The correlation between ERBE/NCEP2 and ERBE/ERA-40 data is also plotted.

Citation: Journal of Climate 19, 17; 10.1175/JCLI3875.1

Table 1.

Models group, name, and resolution used in the analysis.

Table 1.
Table 2.

Coefficients m1 to m4 of the regression model Ĉ′ = f (ω′, [ω]) = m1 + m2ω′ + m3[ω] + m4ω′[ω] + m5ωω′ + m6[ω][ω] for ERBE/ERA-40, ERBE/NCEP2 data, and IPCC model results. Units of Ĉ′ and ω are W m−2 and Pa s−1, respectively.

Table 2.
Table 3.

Correlation r and MSD (in W2 m−4) between the ERBE/ERA-40 data, ERBE/NCEP2 data, and IPCC models for the ([ω]-ω′-Ĉ′) and ([h]-h′-Ĉ′) distributions given in Figs. 3 and 8.

Table 3.
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